Growth rates of unbounded orbits in non-periodic twist maps and a theorem by Neishtadt

Markus Kunze, Mathematisches Institut der Universit¨at K¨oln

Abstract: We consider twist maps on the plane (like the ping-pong map) with non-periodic angles, where typically bounded and unbounded motions co-exist. For the latter case we prove a theorem which shows that in the analytic setting the growth rate is at most logarithmic, and furthermore an example of a system is given where all orbits grow at this rate. Moreover, we determine the optimal growth rate for a ping-pong with finite regularity.